Small perturbations of polytopes
arXiv:2303.18033 · doi:10.1016/j.jfa.2024.110644
Abstract
Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.
30 pages, 3 figures, accepted manuscript